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I know this world is ruled by infinite intelligence. Everything that surrounds us- everything... Video
Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze.
James Joseph Sylvester
Society is indeed a contract. Subordinate contracts for objects of mere occasional interest may be dissolved at pleasure â€” but the state ought not to be considered as nothing better than a partnership agreement in a trade of pepper and coffee, calico or tobacco, or some other such low concern, to be taken up for a little temporary interest, and to be dissolved by the fancy of the parties. It is to be looked on with other reverence; because it is not a partnership in things subservient only to the gross animal existence of a temporary and perishable nature. It is a partnership in all science; a partnership in all art; a partnership in every virtue, and in all perfection. As the ends of such a partnership cannot be obtained in many generations, it becomes a partnership not only between those who are living, but between those who are to be born. Each contract of each particular state is but a clause in the great primaeval contract of eternal society, linking the lower with the higher natures, connecting the visible and the invisible world, according to a fixed compact sanctioned by the inviolable oath which holds all physical and all moral natures, each in their appointed place. This law is not subject to the will of those, who by an obligation above them, and infinitely superior, are bound to submit their will to that law. The municipal corporations of that universal kingdom are not morally at liberty at their pleasure, and on their speculations of a contingent improvement, wholly to separate and tear asunder the bands of their subordinate community, and to dissolve it into an unsocial, uncivil, unconnected chaos of elementary principles. It is the first and supreme necessity only, a necessity that is not chosen, but chooses, a necessity paramount to deliberation, that admits no discussion, and demands no evidence, which alone can justify a resort to anarchy. This necessity is no exception to the rule; because this necessity itself is a part too of that moral and physical disposition of things, to which man must be obedient by consent or force: but if that which is only submission to necessity should be made the object of choice, the law is broken, nature is disobeyed, and the rebellious are outlawed, cast forth, and exiled, from this world of reason, and order, and peace, and virtue, and fruitful penitence, into the antagonist world of madness, discord, vice, confusion, and unavailing sorrow.
You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.
God exists since mathematics is consistent, and the Devil exists since we cannot prove it.
I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
You may assume infinite ignorance and unlimited intelligence.
I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God. I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not â€” I do not say divisible â€” but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.
Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.
Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
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